ok so i read that Duration is calculated by drawing a tangent to the price/yield curve of a bond… so i took a hypothetical bond which pays 3 annual coupons of 100 each and par value 1000… the equation of the price than is price=100/y+100/y^2+1100/y^3… differentiating it gave me the result… -100/y^2-200/y^3-3300/y^4… since y is the discount rate factor and discounting factors are read as % i.e 10=.10 i divided the entire equation by 100 … than i assumed two discounting rates,10% and 11% and found out the value of the bond using the full valuation model and the results were 1000 and 975.56…i.e a fall in the value = 24.46 now insertng y=1.1 in the differentiated equation the change in value was 24.8 (pretty close to the real fall in value)… so is that how the formula for modified duration was derived which is weighted average of coupon payments and there p.v divided by periodic YTm factor… although my model couldnt derive the exact formula i came a bit close… and sorry for the offtrack question…
It isn’t. Whoever told you that is wrong. Dead wrong.
If duration measured the price change (_ dP _ for you calculus buffs), this would be true. But that’s not what duration measures; it measures the percentage price change (_ dP/P _). If you really want to think about it as a tangent line, then the curve is not the price curve, but the ln(price) curve (natural log of price). Take my word for it, you don’t want to go there.
Sorry you did all that work. It’s useless for the CFA exam, but it builds character. You now, officially, have lots of character.